Experimental study on the wave-induced dynamic response and hydrodynamic characteristics of a submerged floating tunnel with elastically truncated boundary condition

Hydrodynamic load and motion response are the first considerations in the structural design of a submerged floating tunnel (SFT). Currently, most of the relevant studies have been based on a two-dimensional model test with a fixed or fully free boundary condition, which inhibits a deep investigation of the hydrodynamic characteristics with an elastic constraint. As a result, a series of difficulties exist in the structural design and analysis of an SFT. In this study, an SFT model with a one-degree-of-freedom vertical elastically truncated boundary condition was established to investigate the motion response and hydrodynamic characteristics of the tube under the wave action. The effect of several typical hydrodynamic parameters, such as the buoyancy-weight ratio, γ, the relative frequency, f/f_N, the Keulegan–Carpenter (KC) number, the reduced velocity, U_r, the Reynolds number, Re, and the generalized Ursell_s number, on the motion characteristics of the tube, were selectively analyzed, and the reverse feedback mechanism from the tube's motion response to the hydrodynamic loads was confirmed. Finally, the critical hydrodynamic parameters corresponding to the maximum motion response at different values of γ were obtained, and a formula for calculating the hydrodynamic load parameters of the SFT in the motion state was established. The main conclusions of this study are as follows: (i) Under the wave action, the motion of the SFT shows an apparent nonlinearity, which is mainly caused by the intensive interaction between the tube and its surrounding water particles, as well as the nonlinearity of the wave. (ii) The relative displacement of the tube first increases and then decreases with increasing values of f/f_N, U_r, KC number, Re, and the generalized Ursell_s number. (iii) γ is inversely proportional to the maximum relative displacement of the tube and the wave force on the tube in its motion direction. (iv) Under the motion boundary condition (as opposed to the fixed boundary condition), the peak frequency of the wave force on the SFT in its motion direction decreases and approaches the natural vibration frequency of the tube, whereas the wave force perpendicular to the motion direction increases. When the incident wave frequency is close to the natural vibration frequency of the tube, the tube resonates easily, leading to an increased wave force in the motion direction. (v) If the velocity in the Morison equation is substituted by the water particle velocity measured when the tube is at its equilibrium position, the inertia coefficient in the motion direction of the tube is linearly related to its displacement, whereas that in the direction perpendicular to the motion direction is logarithmically related to its displacement.     

Vortex-induced vibration of a tension leg platform tendon: Multi-mode limit cycle oscillations

This paper studies the application of mathematical models to analyze the vortex-induced vibrations of the tendons of a given TLP along the Indian coastline, by using an analytical approach, analyzed using MATLAB. The tendon is subjected to a steady current load, which causes vortex-shedding downstream, leading to cross-flow vibrations. The magnitude of the excitation (lift and drag coefficients) depends on the vortex-shedding frequency. The resulting vibration is studied for possible resonant behavior. The excitation force is quantified empirically, the added mass by potential flow hydrodynamics, and the vibration by normal mode summation method. Non-linear viscous damping of the water is considered. The non-linear oscillations are studied by the phase-plane method, investigating the limit-cycle oscillations. The stable/unstable regions of the dynamic behavior are demarcated. The modal contribution to the total deflection is studied to establish the possibility of resonance of one of the wet modes with the vortex-shedding frequency.     

Vortex-induced vibration (VIV) dynamics of a tensioned flexible cylinder subjected to uniform cross-flow

This paper presents the experimental results of a study on the effects of axial applied tension on the vibration amplitude, the suppression of vibration, hydrodynamic force coefficients and in-line (IL) and cross-flow (CF) frequency responses during vortex-induced vibration of a horizontally mounted flexible cylinder with a low mass ratio (cylinder’s mass/mass of displaced water), low bending-stiffness, and high aspect ratio (length/diameter 200) in the subcritical Reynolds number regime (Re = 1000–16000). The effect of tension is studied by applying four different tensions. It was revealed that higher applied tensions, which reduce the vibration amplitude, could significantly raise the hydrodynamic lift force coefficient. In addition, higher applied tensions generate narrower lock-in bandwidths. After the highest vibration amplitude and during the region of lower vibration amplitudes, within the first lock-in region (in the first mode of vibration), power spectral densities show broad bandwidth, while within other regions and higher modes they appear narrow-banded. The ratio of the dominant IL to CF frequency is approximately equal to 2.0, except for the lower reduced velocities, where the ratio values reach 3.83 for the highest tension accompanied by widening of the region in which this ratio is over 2.0. This ratio is 2.76 for the lowest applied tension with a narrower region.     

Hydrodynamic damping of a circular cylinder at low KC: Experiments and an associated model

This paper investigates the hydrodynamic damping of a smooth circular cylinder undergoing forced oscillations at Keulegan-Carpenter (KC) numbers smaller than 5 and Reynolds (Re) numbers from 10³–10⁵ with and without background steady currents. A series of experiments are conducted with a circular cylinder oscillating in still water, in-line currents and cross currents. The measured drag coefficients of the smooth cylinder in the still water condition match with the well-published results and the theoretical solution of Stokes and Wang at very small KC numbers. The hydrodynamic damping increases with the in-line steady current whereas it remains almost constant at small transverse velocities and increases notably when the latter becomes large. To predict the hydrodynamic damping in in-line steady currents, the performance of the Morison equation based on relative velocity and independent velocity is explored, respectively. The latter model, by separating the drag into two independent parts, leads to a better fit of the drag force than the former, which is not surprising. However, the former is still a preferable option for engineering design due to its simplicity. The experimental data suggest that the existing design guidelines such as ISO-19902 or DNVGL-RP-C205 should be used with caution for KC < 5.     

Slow drift damping force acting on a horizontal cylinder

The hydrodynamic forces acting on a circular cylinder and a rectangular cylinder undergoing slow drift oscillation in regular waves were investigated experimentally and numerically. Forced oscillation tests with low frequency and large amplitude in regular waves and forced two-harmonic oscillation with combined low and high frequencies were carried out in the experimental study. In the numerical study a finite-difference method was used to simulate viscous flow around a two-dimensional oscillating cylinder. The results of experiments showed that a horizontal rectangular cylinder oscillating slowly in waves has much higher damping coefficients than one oscillating in two-harmonic mode, while the numerical study indicated that such differences in the damping coefficient arise partly from the different effects of one-direction harmonic flow and rotating flow on the vortex shedding caused by the slow drift oscillation.     

鹰式波浪能发电装置水动力学性能分析及优化

根据牛顿第二定律,对鹰式波浪能装置多个浮体进行了力学分析,基于微波理论,通过每个浮体之间三种模态的运动耦合,建立了流体力、阻尼力、铰接力、静水回复力等内外力之间的力学方程组。通过以运动浮体为边界条件求解多个浮体的水动力学参数,代入方程组中计算求得最优外加阻尼和最优俘获宽度比,从而优化设计方案,得到此时各浮体在纵荡、垂荡和纵摇三种运动模态下的位移幅值,以及阻尼力、铰接力、液压缸运动速度等相关参数。研究成果为鹰式波浪能装置的设计及制造提供了理论参考和依据。     

基于LES方法圆柱绕流三维数值模拟(英文)

采用计算流体软件CFX5中large.eddy simulation(LES)模型计算了均匀流场中三维圆柱绕流的水动力特性.使用有限体积法对三维N-S方程进行求解.数值模拟着重研究了高雷诺数时展向各截面的压力、阻力、升力及涡管特性.数值计算结果表明:展向各截面柱体受力关于中截面对称且小于二维情况,柱体周围流场呈现明显的三维特性.     

亚临界区雷诺数下电磁力控制圆柱绕流场特性研究

采用脱体涡模拟方法对弱电解质中电磁力作用下圆柱绕流场及其升阻力特性进行了数值模拟与分析。研究结果表明,在亚临界区雷诺数下电磁力可以提高圆柱体边界层内的流体动能,延缓圆柱体近壁面流动分离,减弱绕流场中流向和展向大尺度涡的强度,减小圆柱体阻力及其升力脉动幅值;当电磁力作用参数大于某个临界值后,流动分离角消失,在圆柱体尾部产生射流现象,电磁力产生净推力作用,出现负阻力现象,而且升力脉动幅值显著减小且接近于零。     

非结构化网格浸入边界法的流固耦合数值模拟(英文)

This paper presents an improved unstructured grid immersed boundary method. The advantages of both immersed boundary method and body fitted grids which are generated by unstructured grid technology are used to enhance the computation efficiency of fluid structure interaction in complex domain. The Navier-Stokes equation was discretized spacially with collocated finite volume method and Euler implicit method in time domain. The rigid body motion was simulated by immersed boundary method in which the fluid and rigid body interface interaction was dealt with VOS (volume of solid) method. A new VOS calculation method based on graph was presented in which both immersed boundary points and cross points were collected in arbitrary order to form a graph. The method is verified with flow past oscillating cylinder.     

弹性支撑低质量比圆柱涡激振动数值模拟

近年来,随着深海石油工业的发展,立管的涡激振动现象越来越受学者们关注.使用RANS方程求解器,并结合SST κ-ω湍流模型,对横向和流向自然频率比为1的低质量比弹性支撑圆柱体的两自由度运动进行了数值模拟,计算雷诺数范围为5 300至32 000.采用四阶Runge-Kutta方法求解柱体的振动方程.并结合近期物理实验结果对升力系数、阻力系数、位移和尾涡模式进行了详细比较和讨论.较好地再现了试验观察到的锁定、迟滞、差拍等现象.     

格子Boltzmann方法在串列双圆柱绕流数值模拟中的应用研究

基于格子Boltzmann方法,对二维静止串列双圆柱绕流进行了数值模拟,并将模拟结果与已有研究结果进行了对比分析。为提高计算效率和计算精度,采用了多块网格耦合算法,并在圆柱曲边界处采用了较为精确的边界处理方法。提取了圆柱的升阻力系数,讨论了圆柱间距对圆柱受力情况和尾流特征的影响。数值模拟在雷诺数Re=200条件下进行,对两圆柱中心间距为1.5~4.0D(D为圆柱直径)之间的典型间距进行了数值模拟,获得了圆柱升阻力系数以及尾流中涡和流线的变化,验证了临界间距的存在,模拟结果和已有研究结果符合得较好。     

考虑涡泄模式的低质量比圆柱涡激运动数值模拟

本文与经典实验进行对比,对二维圆柱在不同来流速度下的涡激运动进行研究。将运动系统简化为质量(m)-弹簧(k)-阻尼(ζ)系统,分析浮式圆柱运动的控制方程并通过4阶Runge-Kutta法求解运动微分方程,借助UDF编程嵌入到Fluent求解器中进行求解,结合动网格技术实现流固耦合,对比Jauvtis和Williamson的经典实验以验证数值模拟的可靠性,再现了SS,2S,2T和2P的涡泄模式。虽得到了与Jauvtis和Williamson物理模型实验相近的一些典型结果,没有做更进一-步的研究,但通过实验数据与数值模拟的对比,能够区别研究相同质量比下其他不同参数对涡激运动特性的影响。对m^*=1的浮式圆柱与低质量比圆柱m^*-2.6进行涡激运动数值模拟研究对比,发现不同约化速度下对运动频率、涡泄模型等涡激运动特性均有不同程度的影响。     

淹没垂直圆柱横摇问题的解析研究

应用匹配特征函数展开法建立了有限水深淹没垂直圆柱横摇问题的解析解,通过与边界元方法的对比验证了该方法的正确性.基于上述模型,对淹没圆柱水动力系数进行了研究,结果表明,在大多数频率下,淹没圆柱的附加质量总是大于同样大小的漂浮圆柱,且在高频段近似为漂浮圆柱附加质量的两倍.当淹没深度较大时,圆柱附加质量趋向干常数,辐射阻尼趋...     

表面粗糙度对立管涡激振动响应影响的试验研究

应用模型试验的方法,研究了表面粗糙度对立管涡激振动响应特性的影响规律,对不同粗糙度条件下立管所受拖曳力、升力、端部张力、漩涡泄放频率、结构振动响应频率、位移响应等参数的变化规律进行了对比分析。结果表明：与立管横向振动相比,立管流向振动更早出现锁定现象,因此当折合速度较低时,立管流向振动的涡激振动响应要大于横向振动。立管张力均存在两个峰值频率,其中一个峰值频率为主导频率,与拖曳力主导频率吻合,由流向涡激振动所产生;另一个峰值频率为主导频率的一半,与升力主导频率吻合,由横向涡激振动所产生。因此可以看出：横向涡激振动与流向涡激振动通过张力作用而相互影响。与光滑立管相比,表面粗糙度降低了立管的涡激振动位移响应,减小了涡激振动的锁定区域,但提高了漩涡泄放频率。对于不同粗糙度下的粗糙立管,随着粗糙度的增加,立管的锁定区域开始点逐渐提前,锁定结束点逐渐推迟,锁定区域逐渐变宽。     

Wave analysis of porous geometry with linear resistance law

The wave diffraction-radiation problem of a porous geometry of arbitrary shape located in the free surface of a fluid is formulated by a set of integral equations, assuming a linear resistance law at the geometry. The linear forces, the energy relation and the mean horizontal drift force are evaluated for non-porous and porous geometries. A geometry of large porosity has an almost vanishing added mass. The exciting forces are a factor of 5–20 smaller compared to a solid geometry. In the long wave regime, the porous geometry significantly enhances both the damping and the mean drift force, where the latter grows linearly with the wavenumber. The calculated mean drift force on a porous hemisphere and a vertical truncated cylinder, relevant to the construction of fish cages, is compared to available published results.     

基于一种固体区域迭代算法的圆柱涡激振动数值计算

利用Fluent平台的用户自定义程序（UDF）以及动网格模型,实现了圆柱运动方程的一种迭代求解算法,分别对层流、湍流状态下,弹性支承圆柱体在一定约化速度下的涡激响应进行了数值模拟,探讨了不同阻尼比对涡激响应的影响。结果表明：采用该迭代求解算法对弹性支承圆柱涡激振动的预测结果较为合理;随着阻尼比的逐渐增加,初始支振幅、升阻力系数时程曲线将由多频率拍振,最终变为单一频率主导的振动,且涡激振幅逐渐减小;除了质量-阻尼比联合参数m*ζ外,阻尼比ζ本身也应作为一个重要的涡激影响参数单独进行考量。     

Effect of mass ratio on hydrodynamic response of a flexible cylinder

The effect of the mass ratio on the flow-induced vibration (FIV) of a flexible circular cylinder is experimentally investigated in a towing tank. A Tygon tube with outer and inner diameters of 7.9 mm and 4.8 mm, respectively, was employed for the study. The tube was connected to a carriage and towed from rest to a steady speed up to 1.6 m/s before slowing down to rest again over a distance of 1.6 m in still water. Reynolds number based on the cylinder’s outer diameter was 800–13,000, and the reduced velocity (velocity normalized by the cylinder’s natural frequency and outer diameter) spanned from 2 to 25. When connected, the cylinder was elongated from 420 mm to 460 mm under an axial pre-tension of 11 N. Based on the cylinder’s elongated length, the aspect ratio (ratio of the cylinder’s length to outer diameter) was calculated as 58. Three mass ratios (ratio of the cylinder’s structural mass to displaced fluid mass, m*) of 0.7, 1.0, and 3.4 were determined by filling the cylinder’s interior with air, water, and alloy powder (nickel-chromium-boron matrix alloy), respectively. An optical method was adopted for response measurements. Multi-frequency vibrations were observed in both in-line (IL) and cross-flow (CF) responses; at high Reynolds number, vibration modes up to the 3^rd one were identified in the CF response. The mode transition was found to occur at a lower reduced velocity for the highest tested mass ratio. The vibration amplitude and frequency were quantified and expressed with respect to the reduced velocity. A significant reduced vibration amplitude was found in the IL response with increasing mass ratios, and only initial and upper branches existed in the IL and CF response amplitudes. The normalized response frequencies were revealed to linearly increase with respect to the reduced velocity, and slopes for linear relations were found to be identical for the three cases tested.     

Towards a model of hydrodynamic damping for a circular cylinder with helical strakes at low KC

This paper investigates the hydrodynamic damping of a circular cylinder with helical strakes at Keulegan-Carpenter (KC) number from 0.07 to 3 in the presence of steady currents. Experiments were performed with a straked cylinder oscillating in either in-line or cross currents over Reynolds number (based on the oscillating velocity amplitude) varying from 1260 to 54,000. With in-line current being present, the measured drag coefficients of the straked cylinder are found to depend on the ratio between the oscillating velocity amplitude and the steady current velocity. This phenomenon is further confirmed by computational fluid dynamics using large-eddy simulations. The drag coefficients obtained from the numerical simulations agree well with the experimentally determined values. Similar phenomenon is observed for the cases with cross background current. Based on the experimental data, empirical formulae are proposed to evaluate drag coefficients. These results are of importance in estimating the resonant motion and the fatigue life of risers, e.g. water intake risers, in the flow regime of low KC. Finally, recommendations are provided for fatigue analysis of risers with helical strakes from the perspective of engineering practice.     

三体船横摇模型试验及其特性分析

三体船在波浪中的横摇特性和优点是三体新船型研发的技术支撑,采用模型试验和理论分析相结合的方法,对三体船横摇运动特性进行探讨。开展三体船静水横摇、正横浪零速波浪横摇模型试验,得出三体船线性、非线性阻尼假设下的横摇阻尼、频率响应和周期。通过横摇响应曲线的分析和对比,得出三体船不同侧体位置下波浪中横摇附加惯量、阻尼和运动响应、周期特性,以及侧体位置对以上各横摇特性影响的规律。研究表明：三体船横摇阻尼远大于常规单体船,而横摇运动幅值响应远小于常规单体船;侧体的横位置对三体船横摇具有显著影响,侧体纵向位置对横摇影响很小。综合考虑运动响应和横摇周期,在不规则波中三体船的横摇比常规单体船缓和得多。     

Analysis of wave-drift damping of a VLFS with shallow draft

Numerical analysis of the wave-drift damping of VLFS as a floating elastic plate is presented. The source distribution method is used to analyze the drift force of the floating plate advancing with low-forward speed in waves. In the analysis, the shallow-draft assumption of the floating body is utilized; this assumption leads to the neglect of the steady disturbance field, which simplifies the analysis to a great extent. The consideration of the elastic deformation is made by modal expansion of the response, and the unit-amplitude radiation potentials are computed for each mode. The numerical results have confirmed that the wave-drift damping will have appreciable magnitude at the frequency region where the slow-drift oscillations are dominant. The formula for the wave-drift damping proposed by Aranha (J Fluid Mech 1996;313:39–54) has been compared with the present numerical results, but fundamental disagreement has been observed as reported by Finne and Grue (J Fluid Mech 1998;357:289–320).